We have studied the reconstruction of the (100) surface of both volumic crystals and thin films of magnetite. We have determined that this reconstruction disappears at around 500°C (depending upon the stoichiometry of the particular sample) through a second order transition which has been simulated with an Ising model, performing predictions on the influence of the reconstruction in the character semimetallic of magnetite, and therefore in its possible use as a source of spin polarized electrons. It has also been observed for the first time both in real space and at the surface the paraelastic-ferroelastic transition of magnetite (Verwey transition), by means of both low energy electron microscopy (in collaboration with the Berkeley National Laboratory) and by STM (through a collaboration initiated with the group of Ulrike Diebold, at the Technical University of Vienna).